The question is:
What if some one excuses other in-spite of getting insult? Is it
dharma to take revenge for getting insult?
People in the the other 3 ashramas, ie., brahmacharya, Vanaprastha and Sannyasa are dependent only people in Grihasta ashrama only.
So it boils down to the fact that it rests on Grihastas as to how to guide the people in remaining ashramas and whether to take revenge, if required.
Sri Krishna says in BG
सुखदुःखे समे कृत्वा लाभालाभौ जयाजयौ।
ततो युद्धाय युज्यस्व नैवं पापमवाप्स्यसि।।2.38।।
Treating happiness and sorrow, gain and loss, and conest and defeat
with eanimity, then engage in battle. Thus you will not incur sin.
Here, battle does not indicate an act of fighting with arms, but also indicates the day to day activities of the people in Grihasta ashrama.
Dharma is very subtle, and changes from place to place,time to time, custom to custom, etc.- Desa, Kala and Patra.
So while discharging the duty of a particular ashrama, one has to think and decide whether it is one's Dharma at that point of time to react to an act or take revenge, etc.
If it is required, one has to react. If it is according to Dharma, then it is not a SIN.
Sri Krishna told Arjuna to take to war path, as it is the Dharma of a person from Warrior class.
If the people in Grihasta ashrama are not in a position to react/take a decision, people in other ashramas will take the lead.
That was why even after taking Sannyasa, Sri Sankara and Swami Vivekananda led an active life of integrating the country.